A Review of the Numerical Methods for Diblock Copolymer Melts

This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts. Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications. The phase-field model, in particular, is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time. In this paper, we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths, limitations, stability, accuracy, and computational efficiency of each method. Traditional approaches such as Fourier spectral methods, finite difference methods and alternating direction explicit methods are reviewed, as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented. In addition, we introduce examples of the phase-field model, which are fingerprint image restoration and 3D printing. These examples demonstrate the extensive applicability of the reviewed methods and models.